Solved.
My directory for holding extensions and the options subdirectory had funny permission settings. chmod-ing them to 775 fixed it. I set up 4.2.1 as a frugal installation and copied parts of the current .iso to its fugal home, but did not notice the permissions were wonky. Now AppBrowser can fetch the extension list and then fetch and install extensions.
A bit more on how I figured it out... I used the command-line AppBrowser 'ab' to try to fetch and install some extensions. After I manually wget-ted the info.lst file of all the extensions I was able to use the command-line AppBrowser to browse the repository and look up dependencies, file lists, and so on for various extensions. However, when I tried to actually fetch and install an extension, I got a message that the permission was invalid. At first I thought it might be a permission issue with the repository server, but then I thought it could be on my local system and checked that. I compared the new 4.2.1 frugal folders with an earlier install and found a difference. Changing to the same permission settings for my TCE directory as the older install fixed it. I wonder if some of the other people's problems with AppBrowser could be the same cause. The "Connection Error" message is rather misleading. I may post a suggestion to avoid this in another thread.